A hybrid numerical method for the phase-field model of fluid vesicles in three-dimensional space

We propose an accurate and robust numerical method for the phase-field model of fluid vesicles. An equilibrium shape of fluid vesicle is obtained by minimizing the bending energy with volume and surface area constraints. We propose a hybrid numerical scheme that combines the Lagrange multiplier and penalty methods for two constraints. The numerical method is based on a nonlinearly stabilized splitting scheme and a direct volume correction algorithm. A large penalty constant is generally required; however, it does not guarantee that the surface area converges to a given value. Thus, we propose an adaptive constraint algorithm for the penalty method. Various numerical examples are performed to demonstrate the accuracy and robustness of the proposed method.